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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e26

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-185.77920000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
-185.77920020 (ANTIGONE)
-185.77920020 (BARON)
-185.77920000 (COUENNE)
-185.77920000 (CPLEX)
-185.77920000 (GUROBI)
-185.77920000 (LINDO)
-185.77920000 (SCIP)
References Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002.
Thakur, L S, Domain Contraction in Nonlinear Programming: Minimizing a Quadratic Concave Objective over a Polyhedron, Mathematics of Operations Research, 16:2, 1990, 390-407.
Source BARON book instance misc/e26
Added to library 03 Sep 2002
Problem type QP
#Variables 2
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature concave
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 4
#Linear Constraints 4
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 8
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 2
#Nonzeros in Diagonal of Hessian of Lagrangian 2
#Blocks in Hessian of Lagrangian 2
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-01
Maximal coefficient 5.0000e+00
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          5        1        0        4        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          3        3        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         11        9        2        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,objvar;

Positive Variables  x1,x2;

Equations  e1,e2,e3,e4,e5;


e1..    0.7*x1 + x2 =L= 6.3;

e2..    0.5*x1 + 0.8333*x2 =L= 6;

e3..    x1 + 0.6*x2 =L= 7.08;

e4..    0.1*x1 + 0.25*x2 =L= 1.35;

e5.. -(-3*sqr(x1) - 5*x1 - 3*sqr(x2) - 5*x2) + objvar =E= 0;

* set non-default bounds
x1.up = 10;
x2.up = 30;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2022-05-24 Git hash: 1198c186
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